Question

F(x)=x2−2

and g(x)=x−1
Step 1 of 2 : Find the formula for (f∘g)(x)
and simplify your answer. Then find the domain for (f∘g)(x)
. Round your answer to two decimal places, if necessary.

Answer 1

To find (f \circ g)(x), substitute g(x) into f(x), resulting in (f \circ g)(x) = x^2 - 2x - 1. The domain of (f \circ g)(x) is all real numbers due to the nature of quadratic functions.

Step-by-step explanation:

To find the formula for (f \circ g)(x), you need to compose the functions f and g. That means you'll substitute g(x) into f(x). Starting with the given functions:

f(x) = x^2 - 2

g(x) = x - 1

The composition of f and g, denoted as (f \circ g)(x), is:

(f \circ g)(x) = f(g(x)) = f(x - 1)

Now, substitute x - 1 into f(x):

(f \circ g)(x) = (x - 1)^2 - 2

Expand and simplify:

(f \circ g)(x) = x^2 - 2x + 1 - 2

(f \circ g)(x) = x^2 - 2x - 1

The domain for the simplified function (f \circ g)(x), which is a quadratic function, is all real numbers, or (-\infty, \infty), since there are no restrictions on x that would prevent the function from being defined.